In that place, Latinius the king kindly accepted him, but he gave his son Latinius in marriage.

Latinus is not the name 'Latinius'. Compare 'Latinus' to, e.g., 'Romanus' or 'Gallus' or 'Graecus'.The gender of filiam is female, not male.You have left out 'ei'. 'Laviniam' does not translate to 'Latinius'.

Aeneas urbem condidit, quam in coniugis honorem Lavinium appellavit

Aenease founded the city, which he named in honor of Latinius.. Don't know what to do with the "in coniugis"

You have to read 'in coniugis honorem' as a whole. Coniugis is the genitive of 'coniunx'.i presume 'Latinius' is a typo for 'Lavinius'

In that place, Latinius the king kindly accepted him, but he gave his son Latinius in marriage.

In addition to Kasper's comments, think about the connection between these two sentences in relation to "atque." It means "and," not "but." This should help clarify the other difficulties in the second half of the sentence.